Liquid-like granular film from granular jet impact
Graphical abstract
Introduction
Numerous natural phenomena such as landslides, avalanches, and debris flows as well as industrial processes such as fluidization (Ge et al., 2007, Verma et al., 2013) and particle transport (Lu et al., 2012, Cong et al., 2013) are associated with granular flows. In the last two decades, granular flows have become a frontier within the field of fluid mechanics, physics, and rheology. Though granular materials are cohesionless and highly dissipative, dynamic phenomena such as the free surface wave (Conway et al., 2003), shear instability (Goldfarb et al., 2002), and Rayleigh-Plateau instability (Prado et al., 2011) have been observed in dense granular flows. These granular collective behaviors, which closely resemble the dynamic phenomena observed in classical liquids, are called liquid-like behaviors. Granular jet impacts are important for many industrial applications such as the pulverized coal gasifier, ink-jet printing, impinging jet grinding, and blast cleaning, and have attracted considerable attention in recent years (Boudet et al., 2004, Boudet et al., 2007, Cheng et al., 2007, Cheng et al., 2014, Huang et al., 2010, Johnson and Gray, 2011, Guttenberg, 2012, Sano and Hayakawa, 2012, Sano and Hayakawa, 2013, Ellowitz et al., 2013).
When a liquid jet impinges on a circular target at normal incidence, a water bell (Clanet, 2000, Clanet, 2001) or thin liquid sheet (Clanet and Villermaux, 2002, Villermaux and Clanet, 2002) will appear. Generally, when some particles collide with a smooth wall they will rebound and be back-scattered. However, a liquid-like granular cone or sheet has also been observed when a dense cohesionless granular jet impacts a circular target (Cheng et al., 2007, Cheng et al., 2014, Ellowitz et al., 2013).
The flow dynamics of liquid jets impinging on a circular target has been studied (Clanet, 2000, Clanet, 2001, Clanet and Villermaux, 2002, Villermaux and Clanet, 2002, Bremond et al., 2007, Bhagat and Wilson, 2016). In addition, the liquid-like behaviors of dense granular jets such as the clustering instability (Möbius, 2006, Royer et al., 2009), capillary waves (Amarouchene et al., 2008, Luu et al., 2013), oscillating instabilities (Liu et al., 2012, Fang et al., 2016), and bubble formations (Lu et al., 2013, Lu et al., 2014) have been intensively investigated. Despite previous research, experimental studies on liquid-like granular sheets from granular jet impact are rare.
Cheng et al. (2007) experimentally investigated the liquid-like granular cone or sheet, and found the opening angle quantitatively agrees with that of the water bell. Their results also indicate that the granular sheet gradually changes to a diffuse spray pattern as the number of particles in the jet decreases. They also found that the particle material and surface roughness, the pushing gas property, and the experimental ambient pressure have little effect on the flow patterns of granular jet impact. Later, they demonstrated the anisotropic characteristic of granular sheets by performing granular jet impacts with noncircular cross sections (Cheng et al., 2014). Their results imply that the solid content ratio of the granular jet plays an important role in the granular sheet (Cheng et al., 2007, Cheng et al., 2014). Huang et al. (2010) used the discrete element modeling (DEM) to simulate the granular jet impact and found that the opening angle of the conical granular sheet is influenced by the particle diameter, jet diameter, and coefficient of restitution. Guttenberg (2012) applied a hard-sphere model to simulate the granular sheet, and found that the opening angle is determined by dissipation of energy during the impact process. Ellowitz et al. (2013) used an experimental method similar to Cheng et al. (2007) along with simulation to study granular jet impact. Their results show that a large dead zone forms over the target and that the surface structure and roughness of the target play an insignificant role in the opening angle. Above investigations have suggested that the liquid-like behavior of granular jet impact primarily results from the rapid particle collisions during impact of the target. Until now, the detailed effects of the solid content ratio of the granular jet and the impact region on formation of the granular sheet have not been determined.
Several researchers have investigated the dynamic behavior of dense granular jets impinging on a large plane. Boudet et al., 2004, Boudet et al., 2007 experimentally studied the dynamics of a granular jet impinging on a large horizontal plane. This work showed that a thin granular sheet forms and then quickly evolves to a thicker sheet with ripples due to granular deposit and jump as a result of the surface friction. They called this phenomenon the granular jump, which is similar to the hydraulic jump of liquid jet impact (Bush and Aristoff, 2003). Johnson and Gray (2011) investigated the granular jump of a granular jet impinging on a large inclined plane. Various flow patterns were characterized in detail, such as steady hydraulic jumps and periodic avalanches. It should be noted that due to the different size of impact surface and granular jet velocities, the mechanism of the granular jump is intrinsically different with the granular sheet. The granular jump mainly results from a reduction and deposition in surface flow due to surface friction, while the granular sheet may be primarily developed due to rapid particle collisions during the impact of the granular jet on the target.
It can be seen from above researches that though the dynamics of the granular cone and sheet have been investigated, study on the influencing factors and underlying mechanisms of the liquid-like granular sheet is not sufficient. Here, dense granular jets impacting a circular target were investigated and a new method of changing the solid content ratio of the granular jet was applied. The effects of the particle diameter, the granular jet diameter, the granular jet velocity, and the solid content ratio of the granular jet on the flow patterns of granular jet impact were investigated. We aim to reveal the formation mechanisms of the liquid-like behavior and diffuse particulate nature of granular jet impact and exploit methods to modulate the flow patterns for engineering applications.
Section snippets
Experimental setup and methods
Fig. 1 shows a sketch of the experimental setup. The original point o is at the center of the target surface. Spherical glass beads (ρp = 2.49 × 1000 kg/m3) with diameters between d = 82 μm and d = 350 μm were packed in a hopper. Granular jets were produced by a push of high pressure air (Cheng et al., 2007, Ellowitz et al., 2013), and impinged on a circular flat target below the jet exit at a fixed normalized impact separation of L/D = 2.5. The target used for each test was a smooth plexiglass surface with
Flow patterns of granular jet impact
Images from the side view of granular jet impact at u0 ∼ 2.5 m/s and D = 4 mm are presented in Fig. 2. It can be observed that for d = 82 μm or 122 μm a thin symmetrical granular film resembling the water bell, a hollow bell-shaped film formed by liquid jet impact (Clanet, 2000, Clanet, 2001), is generated after the granular jet impact (animation M1 of Supplemental Material). At d = 184 μm, some particles escape from the granular film and become scattered. As the particle diameter increases to 246 μm or 350
Discussion
The study of the underlying mechanisms for liquid-like granular film formation from granular jet impact is not sufficient. Results of Cheng et al. (2007) have indicated that the parameter D/d plays a determining role in the granular jet impact. However, the current study finds that the granular film will also evolve to the diffuse pattern with decreasing xp at fixed D/d. Thus both xp and D/d, which quantify the interparticle space and the particle number in the granular jet and affect the
Conclusions
In this paper, the behavior of liquid-like granular films from granular jet impact is experimentally and numerically studied, and a new method of changing the solid content ratio of the granular jet is applied to modulate flow patterns. The effects of the granular jet velocity, the particle diameter, the jet diameter, and the solid content ratio of the granular jet on flow patterns of granular jet impact are investigated. Two regimes are identified: the thin liquid-like granular film and the
Acknowledgments
This study was supported by the National Natural Science Foundation of China (91434130) and the Fundamental Research Funds for the Central Universities (WB1516016).
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